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Maximum‐entropy method as a routine tool for determination of particle size distributions by small‐angle scattering
Author(s) -
Tatchev Dragomir,
Kranold Rainer
Publication year - 2004
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889803023069
Subject(s) - fourier transform , scattering , small angle x ray scattering , particle size , particle size distribution , small angle scattering , limiting , computational physics , principle of maximum entropy , optics , materials science , transmission electron microscopy , physics , statistical physics , mathematics , chemistry , mathematical analysis , statistics , mechanical engineering , engineering
Several aspects of the application of the maximum‐entropy method (MEM) to the determination of particle size distributions by small‐angle scattering (SAS) are discussed. The `historic' version of the MEM produces completely satisfying results. Limiting the data error from below ( i.e. imposing a minimal relative error) is proposed as a solution of some convergence problems. The MEM is tested against the Fourier transform technique. The size distribution of Pb particles in an Al–Pb alloy is determined by the MEM and the Fourier transform technique. The size distributions obtained by transmission electron microscopy (TEM) and SAXS show partial agreement.